Continuity mistake: When Howard is on the mound, the shot from behind the plate shows a player ready to catch the ball in a uniform shirt. The next long shot from the stands shows a catcher in full gear, and then back to behind the plate to the player in uniform shirt only.
Character mistake: When Howard is asking Sheldon engineering questions, the first question is "How do you quantify the strength of materials?" Sheldon answers "Young's Modulus," and Howard admits that is correct. But it's not correct - Young's Modulus quantifies a material's elasticity, not strength. (00:17:10)
Continuity mistake: In this episode Leonard has a snoring problem (a result of a deviated septum, which in all probability he was born with, plus Amy says Sheldon has always complained about Leonard's snoring, and Sheldon says after 5 or 6 years he's gotten use to Leonard's snoring), but in episode 14 of season 3 when Sheldon brings up snoring Penny says, "Leonard doesn't snore." And in episode 8 of season 6, Sheldon lists not snoring as one of Leonard's positive traits.